Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves

Tanja Lange

Paper 2002/147

Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves

Tanja Lange

Abstract

We investigate formulae to double and add in the ideal class group of a hyperelliptic genus 2 curve avoiding inversions. To that aim we introduce a further coordinate in the representation of a class in which we collect the common denominator of the usual 4 coordinates. The analysis shows that this is practical and advantageous whenever inversions are expensive compared to multiplications like for example on smart cards.

Note: An updated, enlarged, and corrected paper has been submitted and can be found on the author's homepage http://www.ruhr-uni-bochum.de/itsc/tanja

Metadata

Available format(s): PDF PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: hyperelliptic curve cryptosystems elliptic curve cryptosystems projective coordinates implementation number theory arithmetic explicit formulae
Contact author(s): lange @ itsc ruhr-uni-bochum de
History: 2003-05-22: last of 2 revisions; 2002-09-27: received; See all versions
Short URL: https://ia.cr/2002/147
License: CC BY

BibTeX

@misc{cryptoeprint:2002/147,
      author = {Tanja Lange},
      title = {Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2002/147},
      year = {2002},
      url = {https://eprint.iacr.org/2002/147}
}